If you're still having trouble on the approach, then there is a good chance you're not making eye contact correctly.

When we talk to people, we are communicating in more than just words, every piece of information we send them is part of communication. Research from Albert Mehrabian suggests that body language and tone of voice make up over 90% of actual communication between people. This is why you need to be conscious of the signals you're sending to others that you're not verbally saying.

Females of higher value will begin to judge you from the second you lay eyes on them. When your eyes meet and you look away, you have already shown signs of passiveness and weakness. These are not traits of a confident, successful male. And females of the type you're going after are undoubtedly attracted to men and manly traits, otherwise they'd all be lesbians. You want to show qualities like confidence, dominance, and manliness.

First things first, it is imperative that you hold her gaze and go into it with the knowledge that you're fucking awesome. What you do after this is all a matter of personal style and twist. I keep a pensive expression on my face the first 2 seconds, and then switch to a smile than can only be described as if I'm seeing her slowly strip her clothes off in front of me. Keeping pensive and not smiling for about 2 seconds is vital. It is characteristic of successful people, as mentioned by Lowndes in her book "How to Talk to Anyone"

The mood you set in your mind is reflected through your actions and how you communicate. Is is vital that you're not worried about her catching you staring at her. On the contrary, you should have the mental state that you caught her staring at you. Because, after all, you did ;)

Eye contact should last about 5 seconds, then communication needs to take place. It has to happen that second or else it will just be awkward...so don't be awkward. It can be verbal or non-verbal. If you can't talk to her, do something funny or just play around with her. Be memorable. Be unique. Catch her attention.

If you do this right, you will almost immediately begin to notice that women are more receptive to having a conversation with you, assuming you're not some ugly fuck that doesn't know how to wash his hair and you know how to keep up with good posture.

But, this is just the first 10 seconds or so. You're on your own that that :P

Edit: I can't stress mental state enough!!! It sets the tone for the entirety of your interaction with someone. It is the absolute primary difference between alpha males and AFC's and it is what makes or breaks your game. When AFC's are contemplating the undesirable consequences of an action, hegemonic males are thinking about how much fun it will be.

I know it's a corny example, but the only difference between Tyler Durden and Jack in Fight Club was, you guessed it!!! The state of mind.

Edit 2: This is Fun. I'll have another one of these next week. Already have some ideas.